Solving Absolute Value Inequalities Practice Set

Front

Define absolute value.

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the general form of an absolute value inequality?

Back

An absolute value inequality can be expressed as |A| < B or |A| > B, where A is an expression and B is a non-negative number.

Front

Solve the absolute value inequality: |x - 4| < 3.

Back

1 < x < 7.

Front

Solve the absolute value inequality: |2x + 1| > 5.

Back

x < -3 or x > 2.

Front

What does it mean when an absolute value inequality is 'greater than'?

Back

It means that the expression inside the absolute value is either greater than a positive number or less than its negative counterpart.

Front

What does it mean when an absolute value inequality is 'less than'?

Back

It means that the expression inside the absolute value is confined between two values, specifically between the negative and positive of that number.

Front

Solve the absolute value inequality: |3x - 2| ≤ 4.

Back

-2/3 ≤ x ≤ 2.

Front

What is the solution set for |x| < a, where a > 0?

Back

The solution set is -a < x < a.

Front

What is the solution set for |x| > a, where a > 0?

Back

The solution set is x < -a or x > a.

Front

Solve the absolute value inequality: |x + 5| ≥ 2.

Back

x ≤ -7 or x ≥ -3.